Least Common Multiple

- - Pre-Algebra

Least Common Multiple HeaderThe least common multiple (LCM) of two or more numbers is the smallest or least number that is divisible by all the given numbers. Hence, for counting numbers p and q, p\times q=GCF\left (p,q\right )\times LCM\left (p,q\right ).

Examples:

1. Find the LCM of 6 and 20.

SOLUTION:

Our LCM is the product of all the quotients and divisors, that is,

LCM=2\times 3\times 10=60 \quad \mbox{or} \quad LCM\left ( 6,20 \right )=60.

2. Find the LCM of 8, 24 and 36.

SOLUTION:

Hence, the least common multiple of 8, 24 and 36 is

LCM=2\times 2\times 3\times 2\times 2\times 3=144 \quad \mbox{or} \quad LCM\left ( 8,24,36 \right )=144.

3. Find the LCM of 2, 5 and 7.

SOLUTION:

The numbers are relatively prime. Their LCM is just their product; that is,

LCM\left ( 2,5,7 \right )=70.

Least Common Multiple Worksheets

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